Research Article s

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

Open AccessResearch Article

Journal of Electrical amp Electronic SystemsJo

urna

l of E

lectrical amp Electronic

Systems

ISSN 2332-0796

Mars et al J Electr Electron Syst 2017 62DOI 1041722332-07961000232

Corresponding author Nadia Mars SPEG ENIG Tunisia Center for Research in Information and Communication Sciences and Technology (CReSTIC) IUT 9 Av Quebec 10000 Troyes France Tel 0021694286002 E-mail nedyamarshotmailfr

Received July 14 2017 Accepted July 25 2017 Published July 27 2017

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Copyright copy 2017 Mars N et al This is an open-access article distributed under the terms of the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original author and source are credited

Synergetic MPPT Controller for Photovoltaic SystemNadia Mars12 Faten Grouz1 Najib Essounbouli2 and Lassaad Sbita1

1Research Unit of Photovoltaic Wind and Geothermal Systems (SPEG) the National Engineering School of Gabes (ENIG) University of Gabes Av Omar Ibn El Khattab Zrig Eddakhlania (6072) Tunisia2Center for Research in Information and Communication Sciences and Technology (CReSTIC) IUT 9 Av Quebec 10000 Troyes France

Keywords PV system Synergetic control Maximum power pointtracking Boost converter PV panel

IntroductionNowadays solar energy has great importance because of its

sustainability and environmental friendly characteristic The photovoltaic module represents the fundamental power conversion unit of PV system the fact that the output characteristic depends on the solar radiation and the cell temperature [1] In order to get the maximum of power from solar panels and enhance the PV systemrsquos efficiency the selection of a maximum power point tracker (MPPT) algorithm is necessary [2]

A significant number of MPPT control systems have been developed for years to extract the maximum power that the photovoltaic module can provide [3] Each MPPT has its own advantages and disadvantages Due to their simplicity perturbation and observation (PampO) algorithm and incremental conductance (IC) method are the most widely used [45] The PampO algorithm consists of perturbing the PV output voltage and observing the output power to determine the peak power direction The IC methods compare between the instantaneous and the incremental conductance to track MPP [6] However these methods have some disadvantages PampO control fails to track the MPP during the rapid solar irradiation changes and IC method around the maximum power point [7]

To solve these problems many solutions have been reported in literature To get better performance to the PV system an adaptive perturbation step size has been proposed [8] This method is effective but it is complex in implementation as it needs the operation point location In addition the implementation of this control is switched between adaptive duty cycle and fixed duty cycle control

There are also other techniques such as fractional short circuit current method [9] and fractional open circuit voltage method [10] However these two methods have a weaker and less accurate performance

In addition a several number of intelligent methods have been adopted to estimate the voltage and the load current values such as fuzzy logic artificial neural networks and genetic algorithms [11-13] Such methods are frequently complex and require considerable knowledge in control system design

Recently sliding mode control (SMC) is used in photovoltaic

systems [1415] SMC is a non-linear control strategy which has several advantages such as robustness good dynamical response and simplicity in its implementation On the other hand its major drawback is a chattering phenomenon Hence this phenomenon induces many undesirable oscillations in control signal [16] Synergetic control (SC) as a solution is proposed in this paper to ensure stability of PV system with fast dynamic response Synergetic control theory is introduced in ref [17] SC like sliding mode control is a non-linear control strategy It allowed changing the system structure by switching from one set of continuous functions of state to another at any instant [18] Synergetic control has the advantage of finite time convergence and tiny steady state error In addition it should achieve similar performance as SMC without chattering phenomenon [19] A MPPT control strategy based on SC has been presented in ref [20] However this algorithm has the drawback such as parameter tuning difficulties and complexity Therefore the aim of this paper is to develop a novel SC scheme that is simple to implement and possesses an excellent steady state performance

Inspired from the above work this paper proposes a novel MPPT using synergetic approach for stand-alone photovoltaic system The outline of the paper is as flows The PV panel model is described in section II Section III presents the mathematical model for a boost DC-DC converter In the following section synergetic approach procedure is exposed and the proposed synergetic MPPT controller is given Section V presents the simulation result and discussion In the last section conclusions are given

Photovoltaic GeneratorHow a PV cell working

Photovoltaic cell is basically a p-n junction which converts directly

AbstractA novel non-linear power point tracking method of photovoltaic system (PV) based on synergetic control strategy

is proposed This technique uses a synergetic control strategy to achieve the maximum power point output without a chattering phenomenon The PV system consists of a PV panel DC-DC boost converter MPPT controller and an output load Synergetic control is easy to implement has controllable dynamics towards the origin and gives a good maximum power operation under environmental changes (solar radiation and PV cell temperature)To show the robustness and validity of this approach a mathematical model is presented and simulated using MatlabSIMULINK under different atmospheric conditions Indeed the simulation results showed the advantages of this new algorithm especially the reduction of the chattering problem

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 2 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

sunlight to electricity When the cell exposed to the sunlight the cell photons are absorbed by the semiconductor atoms freeing electrons from the negative layer These electrons find their path through an external circuit toward the positive layer resulting an electric current [2122] Monocrystalline polycrystalline and thin film technologies are the major families of PV cells The absorption depends mainly on the cell surface semiconductor or band gap the temperature and the solar radiation [23]

PV panel model

To model the PV Panel the scientific community offer several models The single diode model is the most classical one described in literature [24] The equivalent circuit (Figure 1) consists of current source to model the incident luminous flux a diode for cell polarisation phenomena a parallel resistance due to leakage current and a series resistance representing various contacts [6]

The general mathematical PV cell equation is given by the following equation [25]

I=IphNp-Id-Ish (1)

Where Iph is a photo current Id is a diode current and Ish a shunt current The module photo-current evaluated as

Iph=Gk [Isc+kI(Top-Tref)] (2)

The shunt current is described by the following equation

pv pv ssh

sh

V I RI

R+

= (3)

The dark current Id is calculated by the following equation

exp 1pv S pvd s

S t

V R II I q

N V +

= minus

(4)

The reserved saturation current varies with temperature is described according to the following equation

3 1 1

op ref

qEgnk T Top

s rsref

TI I e

T

minus

=

(5)

Finally the output current can be expressed as

exp 1pv S pv pv pv Sp ph p s p

S t Sh

qV R I V I RI N I N I N

N V R + +

= minus minus minus

(6)

An ideal PV cell has very high equivalent shunt resistance and very low equivalent series resistance (Simplification Rsh gtgtgt Rs)

Equation (1) with Rs=0 and Rsh=infin becomes

exp 1pvp ph p s

S

AVI N I N I

N n

= minus minus

(7)

PV characteristics

The PV panel specifications used for simulations are presented in Table 1

Figure 2 shows the typical current versus voltage and power versus voltage curves for the photovoltaic module Figures 3 and 4 show the I-V and P-V characteristics of PV module under different temperature levels (fixed irradiance) Figures 5 and 6 show the I-V and P-V characteristics of PV module under different solar radiation levels (fixed temperature) [20]

It is clear that the PV module inherits nonlinear characteristics at its MPP This MPP varies with temperature and irradiance Hence PV panel power increases with irradiance increasing or temperature decreasing Therefore in order to ensure that the photovoltaic system work at its MPP a control algorithm is needed

0 5 10 15 20 250

50

Voltage (V)

)W( rewop

0

2

4

Curre

nt (A

)

MPP Maximum power point

Vmp

Imp

Pmp

Short circuit current Isc

Open circuit voltageVoc

Figure 2 I-V and P-V characteristic curves at a fixed irradiation (G=1000Wm2) and a fixed temperature (T=25degC)

0 5 10 15 20 250

10

20

30

40

50

60

Voltage (V)

)W( rewoP

T=0degCT=25degCT=50degCT=75degC

Figure 3 Power-Voltage curve in different temperature (G=1000Wm2)Figure 1 Equivalent circuit of solar cell

Maximum power (Pmax) 60 WOpen-circuit voltage (Voc) 211 VShort-circuit current (Isc) 38 AOptimum operating voltage (Vmpp) 171 VOptimum operating current (Impp) 35 A

Table 1 Specifications of PV Panel

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 3 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

DC-DC ConverterIn order to extract the maximum power from the PV module

the DC-DC converter allows adaptation between the PV module and the load [3] Figure 7 shows the circuit of the boost converter whose output voltage (V0) is more than or equal to the input voltage Vpv (PV generator voltage)

The switch S operates at a high frequency to produce a chopped output voltage [26] The power flow is controlled by adjusting the ON and off of the switching Hence When S=1 the switch is ON The equations can be written as

00

1 ( )1

1

1 1( )2 2

pvpv L

Lpv

L L

dVi i

dt CdI Vdt L

dV i i idt C C

= minus

=

= minus

(8)

When S=0 the switch is OFF the equation can be expressed in equation

0

00

1 ( )1

1 1

1 ( )2

pvpv L

Lpv

L

dVi i

dt CdI V Vdt L L

dV i idt C

= minus

= minus

= minus

(9)

The boost converter can be used to drive a high voltage load from a low voltage PV module The dynamic model of the used boost converter can be derived as

0

00

1 ( )1

1 1 ( 1)

1 1( )2 2

pvpv L

Lpv

L L

dVi i

dt CdI V S Vdt L L

dV i i Sidt C C

= minus

= + minus

= minus minus

(10)

If we set x=[x1 x2 x3]Tr=[Vpv iL V0]

Tr

With Tr matrix transpose the above expression can be written as

( ) ( )dxx f x t g x t Sdt

= = + (11)

Where

0 0

0

0

1 ( ) 011 1 ( ) ( ) ( )

1 1( )2 2

p L

pv

L pv

L L

i iCV

x i f x V V g x VL L

Vi i i

C C

minus = = minus = minus minus

0 5 10 15 20 250

05

1

15

2

25

3

35

4

Voltage (V)

)A( tnerruC

T=0degCT=25degCT=50degCT=75degC

Figure 4 Current-Voltage curve in different temperature (G=1000Wm2)

0 5 10 15 20 250

10

20

30

40

50

60

Voltage (V)

)W( rewoP

G=1000Wm2G=700Wm2G=400Wm2G=200Wm2

Figure 5 Power-Voltage curve in different irradiance (T=25degC)

0 5 10 15 20 250

05

1

15

2

25

3

35

4

Voltage (V)

)A( tnerruC

G=1000Wm2G=700Wm2G=400Wm2G=200Wm2

Figure 6 Current-Voltage curve in different irradianceVpv

iL

iC2VL

Cr CrS

L i0

V0

Figure 7 Diagram of boost converter

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 4 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

Synergetic MPPT ControllerSynergetic control procedure

The general synergetic control procedure is reviewed in this section Synergetic control theory is a nonlinear approach it uses a non-linear model of the power system to overcome the above mentioned problems of the linear controls [27] The nonlinear differential equation of the system can be described by the following form [2829]

( )dxx f x s tdt

= =

(12)

Where x=(x1x2hellipxn) is the state variable vector of size n s=(s1s2hellipsm) is the control input of size m=1 and t is time

The SC approach is based on a particular choice of the macro variable Therefore we started by defining a nonlinear macro-variable as follows

Ψ=Ψ(xt) (13)

The controller objective is to force the system to operate the manifold (Ψ=0) However using the same procedure as in the synergetic approach [3031] The macro-variable can be a simple linear combination of the state variables Hence the designer can select the characteristics of this macro-variable according to the control specifications such as the settling time and the control objective The desired dynamic evolution of the macro-variable is

0 0T TΨ +Ψ =

(14)

Where T is a specific designer chosen that determines the rate of convergence speed to the manifold specified by the macro-variable Taking into account the chain rule of differentiation that is given by

d xdxΨ

Ψ =

(15)

Combining 12 14 and 15

( ) 0dT f x s tdxΨ

+Ψ = (16)

Finally upon solving equation 16 the control law can be described as flow

[ ( ) ]S x t x t Tδ= Ψ (17)

As can be seen the control output S depends not only on the system state variables but also on the time constant T and the macro variable Ψ as well giving the designer latitude to choose the characteristics of the controller by selecting a suitable macro-variable and a constant time T By suitable selection of macro-variable the designer can obtain many interesting characteristics such as

bull Stability

bull Noise suppression

bull Parameters ffinsensffitffivffity

The procedure summarized here can be performed by hand for simple systems such as the DC-DC boost converter used for this study which has a small number of state variables

Synergetic MPPT controller

Maximum power point tracking is an essential stage of a photovoltaic system for tracking the maximum power The system studied in this paper is a stand-alone PV system As shown in Figure 8

it consists of a PV panel a DC-DC converter a load and a synergetic controller

Like all other MPPT the modelling of the synergetic MPPT controller is based on the output power of the cell which is P=VI The optimisation of the output power is achieved as shown in Figure 2 by selecting the manifold as

0PVpart

=part

(18)

Hence the manifold is defined asP IV IV Vpart part

Ψ = = +part part

(19)

In studied DC-DC boost converter there are two states the output voltage (x1) and the inductor current (x2) As Ψ is function of x1 only hence the chain rule of differentiation becomes

2

22d I IV V Vdx V V

Ψ part partΨ = = + part part (20)

Then the desired dynamic evolution of the macro-variable can be expressed

0 0T TΨ +Ψ = ge (21)

So

2

22 0I I IT V V V IV V V

part part part+ + + = part part part

(22)

20 0

2

12

IV IV VdV V I I V

L V V

part+

part= minus = part part

+ part part

(23)

Stability proof

Based on Lyapunov function the macro-variable requires that

21 0 0 02

dV VdxΨ

= Ψ = Ψ = ΨΨ

(24)

Results and DiscussionThe PV model system has been implemented in MatlabSimulink

shown in Figure 9 which includes the PV array the DC-DC boost converter with an MPPT controller connected to a load The PV modules specificationsrsquo are shown in Table 1The converter circuit topology is designed to be compatible with given load to achieve the maximum power transfer from the solar panel The MPPT system specificationrsquo used in the simulation is shown in Table 2

PV Panel

V

I

Sw

V0

LOAD

Synergetic MPPTController

GT

Figure 8 Block diagram of PV system with synergetic controller

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 5 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

G

T

V

G

T

I I

V

Sw

[I]

[V]

PV Module

I

Sw

Boost ConverterSynergetic

MPPT controller

[V]

[I]X

Pout

Vpv

V0

I0

[V]V

V0

I0

Figure 9 Simulation diagram of the stand-alone PV system

6 7 8 9 10

x 10-3

58

60

62

0 0002 0004 0006 0008 001 0012 0014 0016 0018 0020

10

20

30

40

50

60

70

Time (S)

Ppv

V0

Vpv

Ipv

(a)

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002-20

0

20

40

60

80

100

Time (S)

elbairav-orcaM

(b)

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002-02

0

02

04

06

08

1

12

Time (S)

elcyc ytuD

(c)

Ppv

(W)

V0

(V)

Vpv

(V)

Ipv

(A)

Figure 10 Simulation with standard condition (a) PpvV0 Vpv and Ipv (b) Duty Cycle and (c) macro variable

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 6 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

To evaluate the effectiveness of proposed MPPT We consider the PV cell with irradiance is 1000Wm2 and temperature is 25degC The simulation results of the output power the PV panel voltage the output voltage and the PV panel current are shown in Figures10a-10c show the duty cycle and the macro-variable

The photovoltaic system is dependent on the temperature and irradiation conditions and the power will be maximum for along the variations of temperature and irradiation in the PV panel which is giving to input to DC-DC converter Therefore we will evaluate the robustness of the proposed MPPT according to temperature and irradiance variation In each figure two different values of temperature

or irradiance are presented in order to show the robustness (Figures 11-14)

All the obtained results show that the use of synergetic MPPT controller is effective The SC ensures very fast convergence to the MPP and there are no oscillations around the MPP Moreover it provides a high robustness with the variation of the external conditions (temperature and solar irradiance)

ConclusionIn this paper a whole PV system with optimal control strategy

has been presented The Synergetic control is formulated and applied to the PV system This system consists of a solar panel DC-DC boost converter synergetic MPPT controller and an output load The effectiveness and the robustness of the proposed MPPT are proven by simulation results

It is proved using Simulation MatlabSimulink that the designed SC showed good results as it successfully and precisely tracked the MPP with a significantly higher efficiency Hence synergetic control eliminates chattering effects and robust to abrupt change of solar radiation and temperature

L 480 (mH)R 5 (Ω)K 138e-23 (JK)Q 16e-19 (C)Rs 018 (Ω)Rp 360 (Ω)N 36T 0003

Table 2 System specifications

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002600

650

700

750

800

850

900

950

1000

1050

1100

Time (S)

)2m

W( ecnaidarrI

Figure 11 Solar irradiance variation

0 0002 0004 0006 0008 001 0012 0014 0016 0018 0020

10

20

30

40

50

60

70

Time (S)

PpvV0VpvIpv

Ppv

(W)

V0

(V)

Vpv

(V)

Ipv

(A)

Figure 12 Simulation with step irradiance change (1000Wm2 T=25degC)

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002295

300

305

310

315

320

325

Time (S)

)K( erutarepmeT

Figure 13 Temperature variation

0 0002 0004 0006 0008 001 0012 0014 0016 0018 0020

10

20

30

40

50

60

70

Time (S)

)A( vpI )V( vpV )V( 0V )W( vpP

PpvV0VpvIpv

Figure 14 Simulation with step irradiance change (1000Wm2 T=25degC)

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 7 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

In further work these results will be experimentally validated

References

1 Kachhiya K Lokhande M Patel M (2011) Matlabsimulink model of solarPV module and MPPT algorithm National Conference on Recent Trends inEngineering and Technology

2 Rao GJ Mangal DK Shrivastava SK Baig MG (2016) Modeling and Simulation of Incremental Conductance Maximum Power Point Tracking (MPPT) Algorithm for Solar PV Array Using Boost Converter IJSRSET

3 Atik L Petit P Sawicki JP Ternifi ZT Bachir G et al (2016) Comparison of four MPPT techniques for PV systems AIP Conference Proceedings 1758(1)10106314959443

4 Zegaoui A Aillerie M Petit P Sawick JP Charles JP et al (2011) Dynamic behaviour of PV generator trackers under irradiation and temperature changes Solar Energy 85 2953-2964

5 Zegaoui A Aillerie M Petit P Sawick JP Jaafar A et al (2011) Comparison of Two Common Maximum Power Point Trackers by Simulating of PV Generators Energy Procedia 6 678-687

6 Belkaid A Gaubert JP Gherbi A (2016) An Improved Sliding Mode Controlfor Maximum Power Point Tracking in Photovoltaic Systems CEAI 18 86-94

7 Gomes de Brito MA Galotto L Sampaio LP Melo GA Canesin CA et al(2013) Evaluation of the Main MPPT Techniques for Photovoltaic Applications IEEE Transactions on Industrial Electronics 60 1156-1167

8 Jiang Y Abu Qahouq JA Haskew TA (2013) Adaptive Step Size withAdaptive-Perturbation-Frequency Digital MPPT Controller for a Single-SensorPhotovoltaic Solar System IEEE Transactions on Power Electronics 28 3195-3205

9 Kollimalla SK Mishra MK (2013) A new adaptive PampO MPPT algorithm basedon FSCC method for photovoltaic system International Conference on Circuits Power and Computing Technologies (ICCPCT) pp 20-21

10 Murtaza AF Sher HA Chiaberge M Boero D Giuseppe MD et al (2013) Anovel hybrid MPPT technique for solar PV applications using perturb amp observe and Fractional Open Circuit Voltage techniques 15th International Conference Mechatronika

11 Esram T Chapman PL (2007) Comparison of Photovoltaic Array MaximumPower Point Tracking Techniques IEEE Transactions on Energy Conversion22 439-449

12 Reisia AR Moradib MH Jamasb S (2013) Classification and comparison of maximum power point tracking techniques for photovoltaic system Renewable and Sustainable Energy Reviews 19 433-443

13 Subudhi B Pradhan R (2013) A Comparative Study on Maximum Power PointTracking Techniques for Photovoltaic Power Systems IEEE Transactions onSustainable Energy 4 89-98

14 Fan L YU Y (2011) Adaptive Non-singular Terminal Sliding Mode Control forDC-DC Converters Advances in Electrical and Computer Engineering 11119-122

15 Romdhane NMB Damak T (2011) Adaptive Terminal Sliding Mode Control for

Rigid Robotic Manipulators International Journal of Automation and Computing 8 215-220

16 Rezkallah M Sharma SK Chandra A Singh B Rousse DR (2017) LyapunovFunction and Sliding Mode Control Approach for the Solar-PV Grid InterfaceSystem IEEE Transactions on Industrial Electronics 64 785-795

17 Kolesnikov AA (2000) Modern applied control theory Synergetic Approach inControl Theory TRTU Moscow Taganrog pp 4477-4479

18 Utkin VI (1977) Variable structure systems with sliding mode IEEE Transactions on Automatic Control 22 212-222

19 Abderrezek H Harmas MN (2016) Comparison study between the terminalsliding mode control and the terminal synergetic control using PSO for DC-DCconverter 4th International Conference on Electrical Engineering (ICEE)

20 Attoui H Khaber F Melhaoui M Kassmi K Essounbouli N (2016) Development and experimentation of a new MPPT synergetic control for photovoltaicsystems Journal of Optoelectronics and Advanced Materials 18 165-173

21 Salmi T Bouzguenda M Gastli A Masmoudi A (2012) MATLABSimulinkBased Modelling of Solar Photovoltaic Cell International Journal of Renewable Energy Research- IJRER

22 Pandiarajan N Muthu R (2011) Mathematical modelling of photovoltaic module with Simulink 1st International Conference on Electrical Energy Systems

23 Kumari JS Babu CS (2012) Mathematical Modeling and Simulation ofPhotovoltaic Cell using Matlab-Simulink Environment International Journal ofElectrical and Computer Engineering (IJECE) 2 26-34

24 Mehimmedetsi B Chenni R (2016) Modelling of DC PV system with MPPT 3rd International Renewable and Sustainable Energy Conference (IRSEC)

25 Ramos-Hernanz JA Campayo JJ Larranaga J Zulueta E Barambones O et al (2012) Two photovoltaic cell simulation models in matlabSimulinkInternational Journal on Technical and Physical Problems of Engineering(IJTPE) 4 45-51

26 Bendiba B Krim F Belmilia H Almia MF Bouloumaa S (2014) Advanced Fuzzy MPPT Controller for a Stand-alone PV System Energy Procedia pp 383-392

27 Jiang Z (2007) Design of power system stabilizers using synergetic control theory IEEE Power Engineering Society General Meeting

28 Laribi M Aiumlt Cheikh MS Larbegraves C Barazane L (2010) Application de lacommande synergetique au controcircle de vitesse drsquoune machine asynchroneRevue des Energies Renouvelables 13 485-496

29 Santi E Monti A Li D Proddutur K Dougal RA (2004) Synergetic Control forPower Electronics Applications A Comparison with the Sliding Mode Approach Journal of Circuits Systems and Computers

30 Santi E Monti A Li D Proddutur K Dougal R (2003) Synergetic control fordc-dc boost converter implementation option IEEE Transactions on industryapplications 39 1803-1813

31 Bezuglov A Kolesnikov A Kondratiev I Vargas J (2005) Synergetic ControlTheory Approach For Solving Systems Of Nonlinear Equations World Multi-Conference Systemics Cybernetics and Informatics

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 2 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

sunlight to electricity When the cell exposed to the sunlight the cell photons are absorbed by the semiconductor atoms freeing electrons from the negative layer These electrons find their path through an external circuit toward the positive layer resulting an electric current [2122] Monocrystalline polycrystalline and thin film technologies are the major families of PV cells The absorption depends mainly on the cell surface semiconductor or band gap the temperature and the solar radiation [23]

PV panel model

To model the PV Panel the scientific community offer several models The single diode model is the most classical one described in literature [24] The equivalent circuit (Figure 1) consists of current source to model the incident luminous flux a diode for cell polarisation phenomena a parallel resistance due to leakage current and a series resistance representing various contacts [6]

The general mathematical PV cell equation is given by the following equation [25]

I=IphNp-Id-Ish (1)

Where Iph is a photo current Id is a diode current and Ish a shunt current The module photo-current evaluated as

Iph=Gk [Isc+kI(Top-Tref)] (2)

The shunt current is described by the following equation

pv pv ssh

sh

V I RI

R+

= (3)

The dark current Id is calculated by the following equation

exp 1pv S pvd s

S t

V R II I q

N V +

= minus

(4)

The reserved saturation current varies with temperature is described according to the following equation

3 1 1

op ref

qEgnk T Top

s rsref

TI I e

T

minus

=

(5)

Finally the output current can be expressed as

exp 1pv S pv pv pv Sp ph p s p

S t Sh

qV R I V I RI N I N I N

N V R + +

= minus minus minus

(6)

An ideal PV cell has very high equivalent shunt resistance and very low equivalent series resistance (Simplification Rsh gtgtgt Rs)

Equation (1) with Rs=0 and Rsh=infin becomes

exp 1pvp ph p s

S

AVI N I N I

N n

= minus minus

(7)

PV characteristics

The PV panel specifications used for simulations are presented in Table 1

Figure 2 shows the typical current versus voltage and power versus voltage curves for the photovoltaic module Figures 3 and 4 show the I-V and P-V characteristics of PV module under different temperature levels (fixed irradiance) Figures 5 and 6 show the I-V and P-V characteristics of PV module under different solar radiation levels (fixed temperature) [20]

It is clear that the PV module inherits nonlinear characteristics at its MPP This MPP varies with temperature and irradiance Hence PV panel power increases with irradiance increasing or temperature decreasing Therefore in order to ensure that the photovoltaic system work at its MPP a control algorithm is needed

0 5 10 15 20 250

50

Voltage (V)

)W( rewop

0

2

4

Curre

nt (A

)

MPP Maximum power point

Vmp

Imp

Pmp

Short circuit current Isc

Open circuit voltageVoc

Figure 2 I-V and P-V characteristic curves at a fixed irradiation (G=1000Wm2) and a fixed temperature (T=25degC)

0 5 10 15 20 250

10

20

30

40

50

60

Voltage (V)

)W( rewoP

T=0degCT=25degCT=50degCT=75degC

Figure 3 Power-Voltage curve in different temperature (G=1000Wm2)Figure 1 Equivalent circuit of solar cell

Maximum power (Pmax) 60 WOpen-circuit voltage (Voc) 211 VShort-circuit current (Isc) 38 AOptimum operating voltage (Vmpp) 171 VOptimum operating current (Impp) 35 A

Table 1 Specifications of PV Panel

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 3 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

DC-DC ConverterIn order to extract the maximum power from the PV module

the DC-DC converter allows adaptation between the PV module and the load [3] Figure 7 shows the circuit of the boost converter whose output voltage (V0) is more than or equal to the input voltage Vpv (PV generator voltage)

The switch S operates at a high frequency to produce a chopped output voltage [26] The power flow is controlled by adjusting the ON and off of the switching Hence When S=1 the switch is ON The equations can be written as

00

1 ( )1

1

1 1( )2 2

pvpv L

Lpv

L L

dVi i

dt CdI Vdt L

dV i i idt C C

= minus

=

= minus

(8)

When S=0 the switch is OFF the equation can be expressed in equation

0

00

1 ( )1

1 1

1 ( )2

pvpv L

Lpv

L

dVi i

dt CdI V Vdt L L

dV i idt C

= minus

= minus

= minus

(9)

The boost converter can be used to drive a high voltage load from a low voltage PV module The dynamic model of the used boost converter can be derived as

0

00

1 ( )1

1 1 ( 1)

1 1( )2 2

pvpv L

Lpv

L L

dVi i

dt CdI V S Vdt L L

dV i i Sidt C C

= minus

= + minus

= minus minus

(10)

If we set x=[x1 x2 x3]Tr=[Vpv iL V0]

Tr

With Tr matrix transpose the above expression can be written as

( ) ( )dxx f x t g x t Sdt

= = + (11)

Where

0 0

0

0

1 ( ) 011 1 ( ) ( ) ( )

1 1( )2 2

p L

pv

L pv

L L

i iCV

x i f x V V g x VL L

Vi i i

C C

minus = = minus = minus minus

0 5 10 15 20 250

05

1

15

2

25

3

35

4

Voltage (V)

)A( tnerruC

T=0degCT=25degCT=50degCT=75degC

Figure 4 Current-Voltage curve in different temperature (G=1000Wm2)

0 5 10 15 20 250

10

20

30

40

50

60

Voltage (V)

)W( rewoP

G=1000Wm2G=700Wm2G=400Wm2G=200Wm2

Figure 5 Power-Voltage curve in different irradiance (T=25degC)

0 5 10 15 20 250

05

1

15

2

25

3

35

4

Voltage (V)

)A( tnerruC

G=1000Wm2G=700Wm2G=400Wm2G=200Wm2

Figure 6 Current-Voltage curve in different irradianceVpv

iL

iC2VL

Cr CrS

L i0

V0

Figure 7 Diagram of boost converter

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 4 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

Synergetic MPPT ControllerSynergetic control procedure

The general synergetic control procedure is reviewed in this section Synergetic control theory is a nonlinear approach it uses a non-linear model of the power system to overcome the above mentioned problems of the linear controls [27] The nonlinear differential equation of the system can be described by the following form [2829]

( )dxx f x s tdt

= =

(12)

Where x=(x1x2hellipxn) is the state variable vector of size n s=(s1s2hellipsm) is the control input of size m=1 and t is time

The SC approach is based on a particular choice of the macro variable Therefore we started by defining a nonlinear macro-variable as follows

Ψ=Ψ(xt) (13)

The controller objective is to force the system to operate the manifold (Ψ=0) However using the same procedure as in the synergetic approach [3031] The macro-variable can be a simple linear combination of the state variables Hence the designer can select the characteristics of this macro-variable according to the control specifications such as the settling time and the control objective The desired dynamic evolution of the macro-variable is

0 0T TΨ +Ψ =

(14)

Where T is a specific designer chosen that determines the rate of convergence speed to the manifold specified by the macro-variable Taking into account the chain rule of differentiation that is given by

d xdxΨ

Ψ =

(15)

Combining 12 14 and 15

( ) 0dT f x s tdxΨ

+Ψ = (16)

Finally upon solving equation 16 the control law can be described as flow

[ ( ) ]S x t x t Tδ= Ψ (17)

As can be seen the control output S depends not only on the system state variables but also on the time constant T and the macro variable Ψ as well giving the designer latitude to choose the characteristics of the controller by selecting a suitable macro-variable and a constant time T By suitable selection of macro-variable the designer can obtain many interesting characteristics such as

bull Stability

bull Noise suppression

bull Parameters ffinsensffitffivffity

The procedure summarized here can be performed by hand for simple systems such as the DC-DC boost converter used for this study which has a small number of state variables

Synergetic MPPT controller

Maximum power point tracking is an essential stage of a photovoltaic system for tracking the maximum power The system studied in this paper is a stand-alone PV system As shown in Figure 8

it consists of a PV panel a DC-DC converter a load and a synergetic controller

Like all other MPPT the modelling of the synergetic MPPT controller is based on the output power of the cell which is P=VI The optimisation of the output power is achieved as shown in Figure 2 by selecting the manifold as

0PVpart

=part

(18)

Hence the manifold is defined asP IV IV Vpart part

Ψ = = +part part

(19)

In studied DC-DC boost converter there are two states the output voltage (x1) and the inductor current (x2) As Ψ is function of x1 only hence the chain rule of differentiation becomes

2

22d I IV V Vdx V V

Ψ part partΨ = = + part part (20)

Then the desired dynamic evolution of the macro-variable can be expressed

0 0T TΨ +Ψ = ge (21)

So

2

22 0I I IT V V V IV V V

part part part+ + + = part part part

(22)

20 0

2

12

IV IV VdV V I I V

L V V

part+

part= minus = part part

+ part part

(23)

Stability proof

Based on Lyapunov function the macro-variable requires that

21 0 0 02

dV VdxΨ

= Ψ = Ψ = ΨΨ

(24)

Results and DiscussionThe PV model system has been implemented in MatlabSimulink

shown in Figure 9 which includes the PV array the DC-DC boost converter with an MPPT controller connected to a load The PV modules specificationsrsquo are shown in Table 1The converter circuit topology is designed to be compatible with given load to achieve the maximum power transfer from the solar panel The MPPT system specificationrsquo used in the simulation is shown in Table 2

PV Panel

V

I

Sw

V0

LOAD

Synergetic MPPTController

GT

Figure 8 Block diagram of PV system with synergetic controller

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 5 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

G

T

V

G

T

I I

V

Sw

[I]

[V]

PV Module

I

Sw

Boost ConverterSynergetic

MPPT controller

[V]

[I]X

Pout

Vpv

V0

I0

[V]V

V0

I0

Figure 9 Simulation diagram of the stand-alone PV system

6 7 8 9 10

x 10-3

58

60

62

0 0002 0004 0006 0008 001 0012 0014 0016 0018 0020

10

20

30

40

50

60

70

Time (S)

Ppv

V0

Vpv

Ipv

(a)

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002-20

0

20

40

60

80

100

Time (S)

elbairav-orcaM

(b)

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002-02

0

02

04

06

08

1

12

Time (S)

elcyc ytuD

(c)

Ppv

(W)

V0

(V)

Vpv

(V)

Ipv

(A)

Figure 10 Simulation with standard condition (a) PpvV0 Vpv and Ipv (b) Duty Cycle and (c) macro variable

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 6 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

To evaluate the effectiveness of proposed MPPT We consider the PV cell with irradiance is 1000Wm2 and temperature is 25degC The simulation results of the output power the PV panel voltage the output voltage and the PV panel current are shown in Figures10a-10c show the duty cycle and the macro-variable

The photovoltaic system is dependent on the temperature and irradiation conditions and the power will be maximum for along the variations of temperature and irradiation in the PV panel which is giving to input to DC-DC converter Therefore we will evaluate the robustness of the proposed MPPT according to temperature and irradiance variation In each figure two different values of temperature

or irradiance are presented in order to show the robustness (Figures 11-14)

All the obtained results show that the use of synergetic MPPT controller is effective The SC ensures very fast convergence to the MPP and there are no oscillations around the MPP Moreover it provides a high robustness with the variation of the external conditions (temperature and solar irradiance)

ConclusionIn this paper a whole PV system with optimal control strategy

has been presented The Synergetic control is formulated and applied to the PV system This system consists of a solar panel DC-DC boost converter synergetic MPPT controller and an output load The effectiveness and the robustness of the proposed MPPT are proven by simulation results

It is proved using Simulation MatlabSimulink that the designed SC showed good results as it successfully and precisely tracked the MPP with a significantly higher efficiency Hence synergetic control eliminates chattering effects and robust to abrupt change of solar radiation and temperature

L 480 (mH)R 5 (Ω)K 138e-23 (JK)Q 16e-19 (C)Rs 018 (Ω)Rp 360 (Ω)N 36T 0003

Table 2 System specifications

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002600

650

700

750

800

850

900

950

1000

1050

1100

Time (S)

)2m

W( ecnaidarrI

Figure 11 Solar irradiance variation

0 0002 0004 0006 0008 001 0012 0014 0016 0018 0020

10

20

30

40

50

60

70

Time (S)

PpvV0VpvIpv

Ppv

(W)

V0

(V)

Vpv

(V)

Ipv

(A)

Figure 12 Simulation with step irradiance change (1000Wm2 T=25degC)

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002295

300

305

310

315

320

325

Time (S)

)K( erutarepmeT

Figure 13 Temperature variation

0 0002 0004 0006 0008 001 0012 0014 0016 0018 0020

10

20

30

40

50

60

70

Time (S)

)A( vpI )V( vpV )V( 0V )W( vpP

PpvV0VpvIpv

Figure 14 Simulation with step irradiance change (1000Wm2 T=25degC)

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 7 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

In further work these results will be experimentally validated

References

1 Kachhiya K Lokhande M Patel M (2011) Matlabsimulink model of solarPV module and MPPT algorithm National Conference on Recent Trends inEngineering and Technology

2 Rao GJ Mangal DK Shrivastava SK Baig MG (2016) Modeling and Simulation of Incremental Conductance Maximum Power Point Tracking (MPPT) Algorithm for Solar PV Array Using Boost Converter IJSRSET

3 Atik L Petit P Sawicki JP Ternifi ZT Bachir G et al (2016) Comparison of four MPPT techniques for PV systems AIP Conference Proceedings 1758(1)10106314959443

4 Zegaoui A Aillerie M Petit P Sawick JP Charles JP et al (2011) Dynamic behaviour of PV generator trackers under irradiation and temperature changes Solar Energy 85 2953-2964

5 Zegaoui A Aillerie M Petit P Sawick JP Jaafar A et al (2011) Comparison of Two Common Maximum Power Point Trackers by Simulating of PV Generators Energy Procedia 6 678-687

6 Belkaid A Gaubert JP Gherbi A (2016) An Improved Sliding Mode Controlfor Maximum Power Point Tracking in Photovoltaic Systems CEAI 18 86-94

7 Gomes de Brito MA Galotto L Sampaio LP Melo GA Canesin CA et al(2013) Evaluation of the Main MPPT Techniques for Photovoltaic Applications IEEE Transactions on Industrial Electronics 60 1156-1167

8 Jiang Y Abu Qahouq JA Haskew TA (2013) Adaptive Step Size withAdaptive-Perturbation-Frequency Digital MPPT Controller for a Single-SensorPhotovoltaic Solar System IEEE Transactions on Power Electronics 28 3195-3205

9 Kollimalla SK Mishra MK (2013) A new adaptive PampO MPPT algorithm basedon FSCC method for photovoltaic system International Conference on Circuits Power and Computing Technologies (ICCPCT) pp 20-21

10 Murtaza AF Sher HA Chiaberge M Boero D Giuseppe MD et al (2013) Anovel hybrid MPPT technique for solar PV applications using perturb amp observe and Fractional Open Circuit Voltage techniques 15th International Conference Mechatronika

11 Esram T Chapman PL (2007) Comparison of Photovoltaic Array MaximumPower Point Tracking Techniques IEEE Transactions on Energy Conversion22 439-449

12 Reisia AR Moradib MH Jamasb S (2013) Classification and comparison of maximum power point tracking techniques for photovoltaic system Renewable and Sustainable Energy Reviews 19 433-443

13 Subudhi B Pradhan R (2013) A Comparative Study on Maximum Power PointTracking Techniques for Photovoltaic Power Systems IEEE Transactions onSustainable Energy 4 89-98

14 Fan L YU Y (2011) Adaptive Non-singular Terminal Sliding Mode Control forDC-DC Converters Advances in Electrical and Computer Engineering 11119-122

15 Romdhane NMB Damak T (2011) Adaptive Terminal Sliding Mode Control for

Rigid Robotic Manipulators International Journal of Automation and Computing 8 215-220

16 Rezkallah M Sharma SK Chandra A Singh B Rousse DR (2017) LyapunovFunction and Sliding Mode Control Approach for the Solar-PV Grid InterfaceSystem IEEE Transactions on Industrial Electronics 64 785-795

17 Kolesnikov AA (2000) Modern applied control theory Synergetic Approach inControl Theory TRTU Moscow Taganrog pp 4477-4479

18 Utkin VI (1977) Variable structure systems with sliding mode IEEE Transactions on Automatic Control 22 212-222

19 Abderrezek H Harmas MN (2016) Comparison study between the terminalsliding mode control and the terminal synergetic control using PSO for DC-DCconverter 4th International Conference on Electrical Engineering (ICEE)

20 Attoui H Khaber F Melhaoui M Kassmi K Essounbouli N (2016) Development and experimentation of a new MPPT synergetic control for photovoltaicsystems Journal of Optoelectronics and Advanced Materials 18 165-173

21 Salmi T Bouzguenda M Gastli A Masmoudi A (2012) MATLABSimulinkBased Modelling of Solar Photovoltaic Cell International Journal of Renewable Energy Research- IJRER

22 Pandiarajan N Muthu R (2011) Mathematical modelling of photovoltaic module with Simulink 1st International Conference on Electrical Energy Systems

23 Kumari JS Babu CS (2012) Mathematical Modeling and Simulation ofPhotovoltaic Cell using Matlab-Simulink Environment International Journal ofElectrical and Computer Engineering (IJECE) 2 26-34

24 Mehimmedetsi B Chenni R (2016) Modelling of DC PV system with MPPT 3rd International Renewable and Sustainable Energy Conference (IRSEC)

25 Ramos-Hernanz JA Campayo JJ Larranaga J Zulueta E Barambones O et al (2012) Two photovoltaic cell simulation models in matlabSimulinkInternational Journal on Technical and Physical Problems of Engineering(IJTPE) 4 45-51

26 Bendiba B Krim F Belmilia H Almia MF Bouloumaa S (2014) Advanced Fuzzy MPPT Controller for a Stand-alone PV System Energy Procedia pp 383-392

27 Jiang Z (2007) Design of power system stabilizers using synergetic control theory IEEE Power Engineering Society General Meeting

28 Laribi M Aiumlt Cheikh MS Larbegraves C Barazane L (2010) Application de lacommande synergetique au controcircle de vitesse drsquoune machine asynchroneRevue des Energies Renouvelables 13 485-496

29 Santi E Monti A Li D Proddutur K Dougal RA (2004) Synergetic Control forPower Electronics Applications A Comparison with the Sliding Mode Approach Journal of Circuits Systems and Computers

30 Santi E Monti A Li D Proddutur K Dougal R (2003) Synergetic control fordc-dc boost converter implementation option IEEE Transactions on industryapplications 39 1803-1813

31 Bezuglov A Kolesnikov A Kondratiev I Vargas J (2005) Synergetic ControlTheory Approach For Solving Systems Of Nonlinear Equations World Multi-Conference Systemics Cybernetics and Informatics

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 3 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

DC-DC ConverterIn order to extract the maximum power from the PV module

the DC-DC converter allows adaptation between the PV module and the load [3] Figure 7 shows the circuit of the boost converter whose output voltage (V0) is more than or equal to the input voltage Vpv (PV generator voltage)

The switch S operates at a high frequency to produce a chopped output voltage [26] The power flow is controlled by adjusting the ON and off of the switching Hence When S=1 the switch is ON The equations can be written as

00

1 ( )1

1

1 1( )2 2

pvpv L

Lpv

L L

dVi i

dt CdI Vdt L

dV i i idt C C

= minus

=

= minus

(8)

When S=0 the switch is OFF the equation can be expressed in equation

0

00

1 ( )1

1 1

1 ( )2

pvpv L

Lpv

L

dVi i

dt CdI V Vdt L L

dV i idt C

= minus

= minus

= minus

(9)

The boost converter can be used to drive a high voltage load from a low voltage PV module The dynamic model of the used boost converter can be derived as

0

00

1 ( )1

1 1 ( 1)

1 1( )2 2

pvpv L

Lpv

L L

dVi i

dt CdI V S Vdt L L

dV i i Sidt C C

= minus

= + minus

= minus minus

(10)

If we set x=[x1 x2 x3]Tr=[Vpv iL V0]

Tr

With Tr matrix transpose the above expression can be written as

( ) ( )dxx f x t g x t Sdt

= = + (11)

Where

0 0

0

0

1 ( ) 011 1 ( ) ( ) ( )

1 1( )2 2

p L

pv

L pv

L L

i iCV

x i f x V V g x VL L

Vi i i

C C

minus = = minus = minus minus

0 5 10 15 20 250

05

1

15

2

25

3

35

4

Voltage (V)

)A( tnerruC

T=0degCT=25degCT=50degCT=75degC

Figure 4 Current-Voltage curve in different temperature (G=1000Wm2)

0 5 10 15 20 250

10

20

30

40

50

60

Voltage (V)

)W( rewoP

G=1000Wm2G=700Wm2G=400Wm2G=200Wm2

Figure 5 Power-Voltage curve in different irradiance (T=25degC)

0 5 10 15 20 250

05

1

15

2

25

3

35

4

Voltage (V)

)A( tnerruC

G=1000Wm2G=700Wm2G=400Wm2G=200Wm2

Figure 6 Current-Voltage curve in different irradianceVpv

iL

iC2VL

Cr CrS

L i0

V0

Figure 7 Diagram of boost converter

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 4 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

Synergetic MPPT ControllerSynergetic control procedure

The general synergetic control procedure is reviewed in this section Synergetic control theory is a nonlinear approach it uses a non-linear model of the power system to overcome the above mentioned problems of the linear controls [27] The nonlinear differential equation of the system can be described by the following form [2829]

( )dxx f x s tdt

= =

(12)

Where x=(x1x2hellipxn) is the state variable vector of size n s=(s1s2hellipsm) is the control input of size m=1 and t is time

The SC approach is based on a particular choice of the macro variable Therefore we started by defining a nonlinear macro-variable as follows

Ψ=Ψ(xt) (13)

The controller objective is to force the system to operate the manifold (Ψ=0) However using the same procedure as in the synergetic approach [3031] The macro-variable can be a simple linear combination of the state variables Hence the designer can select the characteristics of this macro-variable according to the control specifications such as the settling time and the control objective The desired dynamic evolution of the macro-variable is

0 0T TΨ +Ψ =

(14)

Where T is a specific designer chosen that determines the rate of convergence speed to the manifold specified by the macro-variable Taking into account the chain rule of differentiation that is given by

d xdxΨ

Ψ =

(15)

Combining 12 14 and 15

( ) 0dT f x s tdxΨ

+Ψ = (16)

Finally upon solving equation 16 the control law can be described as flow

[ ( ) ]S x t x t Tδ= Ψ (17)

As can be seen the control output S depends not only on the system state variables but also on the time constant T and the macro variable Ψ as well giving the designer latitude to choose the characteristics of the controller by selecting a suitable macro-variable and a constant time T By suitable selection of macro-variable the designer can obtain many interesting characteristics such as

bull Stability

bull Noise suppression

bull Parameters ffinsensffitffivffity

The procedure summarized here can be performed by hand for simple systems such as the DC-DC boost converter used for this study which has a small number of state variables

Synergetic MPPT controller

Maximum power point tracking is an essential stage of a photovoltaic system for tracking the maximum power The system studied in this paper is a stand-alone PV system As shown in Figure 8

it consists of a PV panel a DC-DC converter a load and a synergetic controller

Like all other MPPT the modelling of the synergetic MPPT controller is based on the output power of the cell which is P=VI The optimisation of the output power is achieved as shown in Figure 2 by selecting the manifold as

0PVpart

=part

(18)

Hence the manifold is defined asP IV IV Vpart part

Ψ = = +part part

(19)

In studied DC-DC boost converter there are two states the output voltage (x1) and the inductor current (x2) As Ψ is function of x1 only hence the chain rule of differentiation becomes

2

22d I IV V Vdx V V

Ψ part partΨ = = + part part (20)

Then the desired dynamic evolution of the macro-variable can be expressed

0 0T TΨ +Ψ = ge (21)

So

2

22 0I I IT V V V IV V V

part part part+ + + = part part part

(22)

20 0

2

12

IV IV VdV V I I V

L V V

part+

part= minus = part part

+ part part

(23)

Stability proof

Based on Lyapunov function the macro-variable requires that

21 0 0 02

dV VdxΨ

= Ψ = Ψ = ΨΨ

(24)

Results and DiscussionThe PV model system has been implemented in MatlabSimulink

shown in Figure 9 which includes the PV array the DC-DC boost converter with an MPPT controller connected to a load The PV modules specificationsrsquo are shown in Table 1The converter circuit topology is designed to be compatible with given load to achieve the maximum power transfer from the solar panel The MPPT system specificationrsquo used in the simulation is shown in Table 2

PV Panel

V

I

Sw

V0

LOAD

Synergetic MPPTController

GT

Figure 8 Block diagram of PV system with synergetic controller

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 5 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

G

T

V

G

T

I I

V

Sw

[I]

[V]

PV Module

I

Sw

Boost ConverterSynergetic

MPPT controller

[V]

[I]X

Pout

Vpv

V0

I0

[V]V

V0

I0

Figure 9 Simulation diagram of the stand-alone PV system

6 7 8 9 10

x 10-3

58

60

62

0 0002 0004 0006 0008 001 0012 0014 0016 0018 0020

10

20

30

40

50

60

70

Time (S)

Ppv

V0

Vpv

Ipv

(a)

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002-20

0

20

40

60

80

100

Time (S)

elbairav-orcaM

(b)

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002-02

0

02

04

06

08

1

12

Time (S)

elcyc ytuD

(c)

Ppv

(W)

V0

(V)

Vpv

(V)

Ipv

(A)

Figure 10 Simulation with standard condition (a) PpvV0 Vpv and Ipv (b) Duty Cycle and (c) macro variable

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 6 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

To evaluate the effectiveness of proposed MPPT We consider the PV cell with irradiance is 1000Wm2 and temperature is 25degC The simulation results of the output power the PV panel voltage the output voltage and the PV panel current are shown in Figures10a-10c show the duty cycle and the macro-variable

The photovoltaic system is dependent on the temperature and irradiation conditions and the power will be maximum for along the variations of temperature and irradiation in the PV panel which is giving to input to DC-DC converter Therefore we will evaluate the robustness of the proposed MPPT according to temperature and irradiance variation In each figure two different values of temperature

or irradiance are presented in order to show the robustness (Figures 11-14)

All the obtained results show that the use of synergetic MPPT controller is effective The SC ensures very fast convergence to the MPP and there are no oscillations around the MPP Moreover it provides a high robustness with the variation of the external conditions (temperature and solar irradiance)

ConclusionIn this paper a whole PV system with optimal control strategy

has been presented The Synergetic control is formulated and applied to the PV system This system consists of a solar panel DC-DC boost converter synergetic MPPT controller and an output load The effectiveness and the robustness of the proposed MPPT are proven by simulation results

It is proved using Simulation MatlabSimulink that the designed SC showed good results as it successfully and precisely tracked the MPP with a significantly higher efficiency Hence synergetic control eliminates chattering effects and robust to abrupt change of solar radiation and temperature

L 480 (mH)R 5 (Ω)K 138e-23 (JK)Q 16e-19 (C)Rs 018 (Ω)Rp 360 (Ω)N 36T 0003

Table 2 System specifications

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002600

650

700

750

800

850

900

950

1000

1050

1100

Time (S)

)2m

W( ecnaidarrI

Figure 11 Solar irradiance variation

0 0002 0004 0006 0008 001 0012 0014 0016 0018 0020

10

20

30

40

50

60

70

Time (S)

PpvV0VpvIpv

Ppv

(W)

V0

(V)

Vpv

(V)

Ipv

(A)

Figure 12 Simulation with step irradiance change (1000Wm2 T=25degC)

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002295

300

305

310

315

320

325

Time (S)

)K( erutarepmeT

Figure 13 Temperature variation

0 0002 0004 0006 0008 001 0012 0014 0016 0018 0020

10

20

30

40

50

60

70

Time (S)

)A( vpI )V( vpV )V( 0V )W( vpP

PpvV0VpvIpv

Figure 14 Simulation with step irradiance change (1000Wm2 T=25degC)

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 7 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

In further work these results will be experimentally validated

References

1 Kachhiya K Lokhande M Patel M (2011) Matlabsimulink model of solarPV module and MPPT algorithm National Conference on Recent Trends inEngineering and Technology

2 Rao GJ Mangal DK Shrivastava SK Baig MG (2016) Modeling and Simulation of Incremental Conductance Maximum Power Point Tracking (MPPT) Algorithm for Solar PV Array Using Boost Converter IJSRSET

3 Atik L Petit P Sawicki JP Ternifi ZT Bachir G et al (2016) Comparison of four MPPT techniques for PV systems AIP Conference Proceedings 1758(1)10106314959443

4 Zegaoui A Aillerie M Petit P Sawick JP Charles JP et al (2011) Dynamic behaviour of PV generator trackers under irradiation and temperature changes Solar Energy 85 2953-2964

5 Zegaoui A Aillerie M Petit P Sawick JP Jaafar A et al (2011) Comparison of Two Common Maximum Power Point Trackers by Simulating of PV Generators Energy Procedia 6 678-687

6 Belkaid A Gaubert JP Gherbi A (2016) An Improved Sliding Mode Controlfor Maximum Power Point Tracking in Photovoltaic Systems CEAI 18 86-94

7 Gomes de Brito MA Galotto L Sampaio LP Melo GA Canesin CA et al(2013) Evaluation of the Main MPPT Techniques for Photovoltaic Applications IEEE Transactions on Industrial Electronics 60 1156-1167

8 Jiang Y Abu Qahouq JA Haskew TA (2013) Adaptive Step Size withAdaptive-Perturbation-Frequency Digital MPPT Controller for a Single-SensorPhotovoltaic Solar System IEEE Transactions on Power Electronics 28 3195-3205

9 Kollimalla SK Mishra MK (2013) A new adaptive PampO MPPT algorithm basedon FSCC method for photovoltaic system International Conference on Circuits Power and Computing Technologies (ICCPCT) pp 20-21

10 Murtaza AF Sher HA Chiaberge M Boero D Giuseppe MD et al (2013) Anovel hybrid MPPT technique for solar PV applications using perturb amp observe and Fractional Open Circuit Voltage techniques 15th International Conference Mechatronika

11 Esram T Chapman PL (2007) Comparison of Photovoltaic Array MaximumPower Point Tracking Techniques IEEE Transactions on Energy Conversion22 439-449

12 Reisia AR Moradib MH Jamasb S (2013) Classification and comparison of maximum power point tracking techniques for photovoltaic system Renewable and Sustainable Energy Reviews 19 433-443

13 Subudhi B Pradhan R (2013) A Comparative Study on Maximum Power PointTracking Techniques for Photovoltaic Power Systems IEEE Transactions onSustainable Energy 4 89-98

14 Fan L YU Y (2011) Adaptive Non-singular Terminal Sliding Mode Control forDC-DC Converters Advances in Electrical and Computer Engineering 11119-122

15 Romdhane NMB Damak T (2011) Adaptive Terminal Sliding Mode Control for

Rigid Robotic Manipulators International Journal of Automation and Computing 8 215-220

16 Rezkallah M Sharma SK Chandra A Singh B Rousse DR (2017) LyapunovFunction and Sliding Mode Control Approach for the Solar-PV Grid InterfaceSystem IEEE Transactions on Industrial Electronics 64 785-795

17 Kolesnikov AA (2000) Modern applied control theory Synergetic Approach inControl Theory TRTU Moscow Taganrog pp 4477-4479

18 Utkin VI (1977) Variable structure systems with sliding mode IEEE Transactions on Automatic Control 22 212-222

19 Abderrezek H Harmas MN (2016) Comparison study between the terminalsliding mode control and the terminal synergetic control using PSO for DC-DCconverter 4th International Conference on Electrical Engineering (ICEE)

20 Attoui H Khaber F Melhaoui M Kassmi K Essounbouli N (2016) Development and experimentation of a new MPPT synergetic control for photovoltaicsystems Journal of Optoelectronics and Advanced Materials 18 165-173

21 Salmi T Bouzguenda M Gastli A Masmoudi A (2012) MATLABSimulinkBased Modelling of Solar Photovoltaic Cell International Journal of Renewable Energy Research- IJRER

22 Pandiarajan N Muthu R (2011) Mathematical modelling of photovoltaic module with Simulink 1st International Conference on Electrical Energy Systems

23 Kumari JS Babu CS (2012) Mathematical Modeling and Simulation ofPhotovoltaic Cell using Matlab-Simulink Environment International Journal ofElectrical and Computer Engineering (IJECE) 2 26-34

24 Mehimmedetsi B Chenni R (2016) Modelling of DC PV system with MPPT 3rd International Renewable and Sustainable Energy Conference (IRSEC)

25 Ramos-Hernanz JA Campayo JJ Larranaga J Zulueta E Barambones O et al (2012) Two photovoltaic cell simulation models in matlabSimulinkInternational Journal on Technical and Physical Problems of Engineering(IJTPE) 4 45-51

26 Bendiba B Krim F Belmilia H Almia MF Bouloumaa S (2014) Advanced Fuzzy MPPT Controller for a Stand-alone PV System Energy Procedia pp 383-392

27 Jiang Z (2007) Design of power system stabilizers using synergetic control theory IEEE Power Engineering Society General Meeting

28 Laribi M Aiumlt Cheikh MS Larbegraves C Barazane L (2010) Application de lacommande synergetique au controcircle de vitesse drsquoune machine asynchroneRevue des Energies Renouvelables 13 485-496

29 Santi E Monti A Li D Proddutur K Dougal RA (2004) Synergetic Control forPower Electronics Applications A Comparison with the Sliding Mode Approach Journal of Circuits Systems and Computers

30 Santi E Monti A Li D Proddutur K Dougal R (2003) Synergetic control fordc-dc boost converter implementation option IEEE Transactions on industryapplications 39 1803-1813

31 Bezuglov A Kolesnikov A Kondratiev I Vargas J (2005) Synergetic ControlTheory Approach For Solving Systems Of Nonlinear Equations World Multi-Conference Systemics Cybernetics and Informatics

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 4 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

Synergetic MPPT ControllerSynergetic control procedure

The general synergetic control procedure is reviewed in this section Synergetic control theory is a nonlinear approach it uses a non-linear model of the power system to overcome the above mentioned problems of the linear controls [27] The nonlinear differential equation of the system can be described by the following form [2829]

( )dxx f x s tdt

= =

(12)

Where x=(x1x2hellipxn) is the state variable vector of size n s=(s1s2hellipsm) is the control input of size m=1 and t is time

The SC approach is based on a particular choice of the macro variable Therefore we started by defining a nonlinear macro-variable as follows

Ψ=Ψ(xt) (13)

The controller objective is to force the system to operate the manifold (Ψ=0) However using the same procedure as in the synergetic approach [3031] The macro-variable can be a simple linear combination of the state variables Hence the designer can select the characteristics of this macro-variable according to the control specifications such as the settling time and the control objective The desired dynamic evolution of the macro-variable is

0 0T TΨ +Ψ =

(14)

Where T is a specific designer chosen that determines the rate of convergence speed to the manifold specified by the macro-variable Taking into account the chain rule of differentiation that is given by

d xdxΨ

Ψ =

(15)

Combining 12 14 and 15

( ) 0dT f x s tdxΨ

+Ψ = (16)

Finally upon solving equation 16 the control law can be described as flow

[ ( ) ]S x t x t Tδ= Ψ (17)

As can be seen the control output S depends not only on the system state variables but also on the time constant T and the macro variable Ψ as well giving the designer latitude to choose the characteristics of the controller by selecting a suitable macro-variable and a constant time T By suitable selection of macro-variable the designer can obtain many interesting characteristics such as

bull Stability

bull Noise suppression

bull Parameters ffinsensffitffivffity

The procedure summarized here can be performed by hand for simple systems such as the DC-DC boost converter used for this study which has a small number of state variables

Synergetic MPPT controller

Maximum power point tracking is an essential stage of a photovoltaic system for tracking the maximum power The system studied in this paper is a stand-alone PV system As shown in Figure 8

it consists of a PV panel a DC-DC converter a load and a synergetic controller

Like all other MPPT the modelling of the synergetic MPPT controller is based on the output power of the cell which is P=VI The optimisation of the output power is achieved as shown in Figure 2 by selecting the manifold as

0PVpart

=part

(18)

Hence the manifold is defined asP IV IV Vpart part

Ψ = = +part part

(19)

In studied DC-DC boost converter there are two states the output voltage (x1) and the inductor current (x2) As Ψ is function of x1 only hence the chain rule of differentiation becomes

2

22d I IV V Vdx V V

Ψ part partΨ = = + part part (20)

Then the desired dynamic evolution of the macro-variable can be expressed

0 0T TΨ +Ψ = ge (21)

So

2

22 0I I IT V V V IV V V

part part part+ + + = part part part

(22)

20 0

2

12

IV IV VdV V I I V

L V V

part+

part= minus = part part

+ part part

(23)

Stability proof

Based on Lyapunov function the macro-variable requires that

21 0 0 02

dV VdxΨ

= Ψ = Ψ = ΨΨ

(24)

Results and DiscussionThe PV model system has been implemented in MatlabSimulink

shown in Figure 9 which includes the PV array the DC-DC boost converter with an MPPT controller connected to a load The PV modules specificationsrsquo are shown in Table 1The converter circuit topology is designed to be compatible with given load to achieve the maximum power transfer from the solar panel The MPPT system specificationrsquo used in the simulation is shown in Table 2

PV Panel

V

I

Sw

V0

LOAD

Synergetic MPPTController

GT

Figure 8 Block diagram of PV system with synergetic controller

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 5 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

G

T

V

G

T

I I

V

Sw

[I]

[V]

PV Module

I

Sw

Boost ConverterSynergetic

MPPT controller

[V]

[I]X

Pout

Vpv

V0

I0

[V]V

V0

I0

Figure 9 Simulation diagram of the stand-alone PV system

6 7 8 9 10

x 10-3

58

60

62

0 0002 0004 0006 0008 001 0012 0014 0016 0018 0020

10

20

30

40

50

60

70

Time (S)

Ppv

V0

Vpv

Ipv

(a)

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002-20

0

20

40

60

80

100

Time (S)

elbairav-orcaM

(b)

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002-02

0

02

04

06

08

1

12

Time (S)

elcyc ytuD

(c)

Ppv

(W)

V0

(V)

Vpv

(V)

Ipv

(A)

Figure 10 Simulation with standard condition (a) PpvV0 Vpv and Ipv (b) Duty Cycle and (c) macro variable

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 6 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

To evaluate the effectiveness of proposed MPPT We consider the PV cell with irradiance is 1000Wm2 and temperature is 25degC The simulation results of the output power the PV panel voltage the output voltage and the PV panel current are shown in Figures10a-10c show the duty cycle and the macro-variable

The photovoltaic system is dependent on the temperature and irradiation conditions and the power will be maximum for along the variations of temperature and irradiation in the PV panel which is giving to input to DC-DC converter Therefore we will evaluate the robustness of the proposed MPPT according to temperature and irradiance variation In each figure two different values of temperature

or irradiance are presented in order to show the robustness (Figures 11-14)

All the obtained results show that the use of synergetic MPPT controller is effective The SC ensures very fast convergence to the MPP and there are no oscillations around the MPP Moreover it provides a high robustness with the variation of the external conditions (temperature and solar irradiance)

ConclusionIn this paper a whole PV system with optimal control strategy

has been presented The Synergetic control is formulated and applied to the PV system This system consists of a solar panel DC-DC boost converter synergetic MPPT controller and an output load The effectiveness and the robustness of the proposed MPPT are proven by simulation results

It is proved using Simulation MatlabSimulink that the designed SC showed good results as it successfully and precisely tracked the MPP with a significantly higher efficiency Hence synergetic control eliminates chattering effects and robust to abrupt change of solar radiation and temperature

L 480 (mH)R 5 (Ω)K 138e-23 (JK)Q 16e-19 (C)Rs 018 (Ω)Rp 360 (Ω)N 36T 0003

Table 2 System specifications

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002600

650

700

750

800

850

900

950

1000

1050

1100

Time (S)

)2m

W( ecnaidarrI

Figure 11 Solar irradiance variation

0 0002 0004 0006 0008 001 0012 0014 0016 0018 0020

10

20

30

40

50

60

70

Time (S)

PpvV0VpvIpv

Ppv

(W)

V0

(V)

Vpv

(V)

Ipv

(A)

Figure 12 Simulation with step irradiance change (1000Wm2 T=25degC)

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002295

300

305

310

315

320

325

Time (S)

)K( erutarepmeT

Figure 13 Temperature variation

0 0002 0004 0006 0008 001 0012 0014 0016 0018 0020

10

20

30

40

50

60

70

Time (S)

)A( vpI )V( vpV )V( 0V )W( vpP

PpvV0VpvIpv

Figure 14 Simulation with step irradiance change (1000Wm2 T=25degC)

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 7 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

In further work these results will be experimentally validated

References

1 Kachhiya K Lokhande M Patel M (2011) Matlabsimulink model of solarPV module and MPPT algorithm National Conference on Recent Trends inEngineering and Technology

2 Rao GJ Mangal DK Shrivastava SK Baig MG (2016) Modeling and Simulation of Incremental Conductance Maximum Power Point Tracking (MPPT) Algorithm for Solar PV Array Using Boost Converter IJSRSET

3 Atik L Petit P Sawicki JP Ternifi ZT Bachir G et al (2016) Comparison of four MPPT techniques for PV systems AIP Conference Proceedings 1758(1)10106314959443

4 Zegaoui A Aillerie M Petit P Sawick JP Charles JP et al (2011) Dynamic behaviour of PV generator trackers under irradiation and temperature changes Solar Energy 85 2953-2964

5 Zegaoui A Aillerie M Petit P Sawick JP Jaafar A et al (2011) Comparison of Two Common Maximum Power Point Trackers by Simulating of PV Generators Energy Procedia 6 678-687

6 Belkaid A Gaubert JP Gherbi A (2016) An Improved Sliding Mode Controlfor Maximum Power Point Tracking in Photovoltaic Systems CEAI 18 86-94

7 Gomes de Brito MA Galotto L Sampaio LP Melo GA Canesin CA et al(2013) Evaluation of the Main MPPT Techniques for Photovoltaic Applications IEEE Transactions on Industrial Electronics 60 1156-1167

8 Jiang Y Abu Qahouq JA Haskew TA (2013) Adaptive Step Size withAdaptive-Perturbation-Frequency Digital MPPT Controller for a Single-SensorPhotovoltaic Solar System IEEE Transactions on Power Electronics 28 3195-3205

9 Kollimalla SK Mishra MK (2013) A new adaptive PampO MPPT algorithm basedon FSCC method for photovoltaic system International Conference on Circuits Power and Computing Technologies (ICCPCT) pp 20-21

10 Murtaza AF Sher HA Chiaberge M Boero D Giuseppe MD et al (2013) Anovel hybrid MPPT technique for solar PV applications using perturb amp observe and Fractional Open Circuit Voltage techniques 15th International Conference Mechatronika

11 Esram T Chapman PL (2007) Comparison of Photovoltaic Array MaximumPower Point Tracking Techniques IEEE Transactions on Energy Conversion22 439-449

12 Reisia AR Moradib MH Jamasb S (2013) Classification and comparison of maximum power point tracking techniques for photovoltaic system Renewable and Sustainable Energy Reviews 19 433-443

13 Subudhi B Pradhan R (2013) A Comparative Study on Maximum Power PointTracking Techniques for Photovoltaic Power Systems IEEE Transactions onSustainable Energy 4 89-98

14 Fan L YU Y (2011) Adaptive Non-singular Terminal Sliding Mode Control forDC-DC Converters Advances in Electrical and Computer Engineering 11119-122

15 Romdhane NMB Damak T (2011) Adaptive Terminal Sliding Mode Control for

Rigid Robotic Manipulators International Journal of Automation and Computing 8 215-220

16 Rezkallah M Sharma SK Chandra A Singh B Rousse DR (2017) LyapunovFunction and Sliding Mode Control Approach for the Solar-PV Grid InterfaceSystem IEEE Transactions on Industrial Electronics 64 785-795

17 Kolesnikov AA (2000) Modern applied control theory Synergetic Approach inControl Theory TRTU Moscow Taganrog pp 4477-4479

18 Utkin VI (1977) Variable structure systems with sliding mode IEEE Transactions on Automatic Control 22 212-222

19 Abderrezek H Harmas MN (2016) Comparison study between the terminalsliding mode control and the terminal synergetic control using PSO for DC-DCconverter 4th International Conference on Electrical Engineering (ICEE)

20 Attoui H Khaber F Melhaoui M Kassmi K Essounbouli N (2016) Development and experimentation of a new MPPT synergetic control for photovoltaicsystems Journal of Optoelectronics and Advanced Materials 18 165-173

21 Salmi T Bouzguenda M Gastli A Masmoudi A (2012) MATLABSimulinkBased Modelling of Solar Photovoltaic Cell International Journal of Renewable Energy Research- IJRER

22 Pandiarajan N Muthu R (2011) Mathematical modelling of photovoltaic module with Simulink 1st International Conference on Electrical Energy Systems

23 Kumari JS Babu CS (2012) Mathematical Modeling and Simulation ofPhotovoltaic Cell using Matlab-Simulink Environment International Journal ofElectrical and Computer Engineering (IJECE) 2 26-34

24 Mehimmedetsi B Chenni R (2016) Modelling of DC PV system with MPPT 3rd International Renewable and Sustainable Energy Conference (IRSEC)

25 Ramos-Hernanz JA Campayo JJ Larranaga J Zulueta E Barambones O et al (2012) Two photovoltaic cell simulation models in matlabSimulinkInternational Journal on Technical and Physical Problems of Engineering(IJTPE) 4 45-51

26 Bendiba B Krim F Belmilia H Almia MF Bouloumaa S (2014) Advanced Fuzzy MPPT Controller for a Stand-alone PV System Energy Procedia pp 383-392

27 Jiang Z (2007) Design of power system stabilizers using synergetic control theory IEEE Power Engineering Society General Meeting

28 Laribi M Aiumlt Cheikh MS Larbegraves C Barazane L (2010) Application de lacommande synergetique au controcircle de vitesse drsquoune machine asynchroneRevue des Energies Renouvelables 13 485-496

29 Santi E Monti A Li D Proddutur K Dougal RA (2004) Synergetic Control forPower Electronics Applications A Comparison with the Sliding Mode Approach Journal of Circuits Systems and Computers

30 Santi E Monti A Li D Proddutur K Dougal R (2003) Synergetic control fordc-dc boost converter implementation option IEEE Transactions on industryapplications 39 1803-1813

31 Bezuglov A Kolesnikov A Kondratiev I Vargas J (2005) Synergetic ControlTheory Approach For Solving Systems Of Nonlinear Equations World Multi-Conference Systemics Cybernetics and Informatics

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 5 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

G

T

V

G

T

I I

V

Sw

[I]

[V]

PV Module

I

Sw

Boost ConverterSynergetic

MPPT controller

[V]

[I]X

Pout

Vpv

V0

I0

[V]V

V0

I0

Figure 9 Simulation diagram of the stand-alone PV system

6 7 8 9 10

x 10-3

58

60

62

0 0002 0004 0006 0008 001 0012 0014 0016 0018 0020

10

20

30

40

50

60

70

Time (S)

Ppv

V0

Vpv

Ipv

(a)

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002-20

0

20

40

60

80

100

Time (S)

elbairav-orcaM

(b)

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002-02

0

02

04

06

08

1

12

Time (S)

elcyc ytuD

(c)

Ppv

(W)

V0

(V)

Vpv

(V)

Ipv

(A)

Figure 10 Simulation with standard condition (a) PpvV0 Vpv and Ipv (b) Duty Cycle and (c) macro variable

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 6 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

To evaluate the effectiveness of proposed MPPT We consider the PV cell with irradiance is 1000Wm2 and temperature is 25degC The simulation results of the output power the PV panel voltage the output voltage and the PV panel current are shown in Figures10a-10c show the duty cycle and the macro-variable

The photovoltaic system is dependent on the temperature and irradiation conditions and the power will be maximum for along the variations of temperature and irradiation in the PV panel which is giving to input to DC-DC converter Therefore we will evaluate the robustness of the proposed MPPT according to temperature and irradiance variation In each figure two different values of temperature

or irradiance are presented in order to show the robustness (Figures 11-14)

All the obtained results show that the use of synergetic MPPT controller is effective The SC ensures very fast convergence to the MPP and there are no oscillations around the MPP Moreover it provides a high robustness with the variation of the external conditions (temperature and solar irradiance)

ConclusionIn this paper a whole PV system with optimal control strategy

has been presented The Synergetic control is formulated and applied to the PV system This system consists of a solar panel DC-DC boost converter synergetic MPPT controller and an output load The effectiveness and the robustness of the proposed MPPT are proven by simulation results

It is proved using Simulation MatlabSimulink that the designed SC showed good results as it successfully and precisely tracked the MPP with a significantly higher efficiency Hence synergetic control eliminates chattering effects and robust to abrupt change of solar radiation and temperature

L 480 (mH)R 5 (Ω)K 138e-23 (JK)Q 16e-19 (C)Rs 018 (Ω)Rp 360 (Ω)N 36T 0003

Table 2 System specifications

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002600

650

700

750

800

850

900

950

1000

1050

1100

Time (S)

)2m

W( ecnaidarrI

Figure 11 Solar irradiance variation

0 0002 0004 0006 0008 001 0012 0014 0016 0018 0020

10

20

30

40

50

60

70

Time (S)

PpvV0VpvIpv

Ppv

(W)

V0

(V)

Vpv

(V)

Ipv

(A)

Figure 12 Simulation with step irradiance change (1000Wm2 T=25degC)

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002295

300

305

310

315

320

325

Time (S)

)K( erutarepmeT

Figure 13 Temperature variation

0 0002 0004 0006 0008 001 0012 0014 0016 0018 0020

10

20

30

40

50

60

70

Time (S)

)A( vpI )V( vpV )V( 0V )W( vpP

PpvV0VpvIpv

Figure 14 Simulation with step irradiance change (1000Wm2 T=25degC)

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 7 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

In further work these results will be experimentally validated

References

1 Kachhiya K Lokhande M Patel M (2011) Matlabsimulink model of solarPV module and MPPT algorithm National Conference on Recent Trends inEngineering and Technology

2 Rao GJ Mangal DK Shrivastava SK Baig MG (2016) Modeling and Simulation of Incremental Conductance Maximum Power Point Tracking (MPPT) Algorithm for Solar PV Array Using Boost Converter IJSRSET

3 Atik L Petit P Sawicki JP Ternifi ZT Bachir G et al (2016) Comparison of four MPPT techniques for PV systems AIP Conference Proceedings 1758(1)10106314959443

4 Zegaoui A Aillerie M Petit P Sawick JP Charles JP et al (2011) Dynamic behaviour of PV generator trackers under irradiation and temperature changes Solar Energy 85 2953-2964

5 Zegaoui A Aillerie M Petit P Sawick JP Jaafar A et al (2011) Comparison of Two Common Maximum Power Point Trackers by Simulating of PV Generators Energy Procedia 6 678-687

6 Belkaid A Gaubert JP Gherbi A (2016) An Improved Sliding Mode Controlfor Maximum Power Point Tracking in Photovoltaic Systems CEAI 18 86-94

7 Gomes de Brito MA Galotto L Sampaio LP Melo GA Canesin CA et al(2013) Evaluation of the Main MPPT Techniques for Photovoltaic Applications IEEE Transactions on Industrial Electronics 60 1156-1167

8 Jiang Y Abu Qahouq JA Haskew TA (2013) Adaptive Step Size withAdaptive-Perturbation-Frequency Digital MPPT Controller for a Single-SensorPhotovoltaic Solar System IEEE Transactions on Power Electronics 28 3195-3205

9 Kollimalla SK Mishra MK (2013) A new adaptive PampO MPPT algorithm basedon FSCC method for photovoltaic system International Conference on Circuits Power and Computing Technologies (ICCPCT) pp 20-21

10 Murtaza AF Sher HA Chiaberge M Boero D Giuseppe MD et al (2013) Anovel hybrid MPPT technique for solar PV applications using perturb amp observe and Fractional Open Circuit Voltage techniques 15th International Conference Mechatronika

11 Esram T Chapman PL (2007) Comparison of Photovoltaic Array MaximumPower Point Tracking Techniques IEEE Transactions on Energy Conversion22 439-449

12 Reisia AR Moradib MH Jamasb S (2013) Classification and comparison of maximum power point tracking techniques for photovoltaic system Renewable and Sustainable Energy Reviews 19 433-443

13 Subudhi B Pradhan R (2013) A Comparative Study on Maximum Power PointTracking Techniques for Photovoltaic Power Systems IEEE Transactions onSustainable Energy 4 89-98

14 Fan L YU Y (2011) Adaptive Non-singular Terminal Sliding Mode Control forDC-DC Converters Advances in Electrical and Computer Engineering 11119-122

15 Romdhane NMB Damak T (2011) Adaptive Terminal Sliding Mode Control for

Rigid Robotic Manipulators International Journal of Automation and Computing 8 215-220

16 Rezkallah M Sharma SK Chandra A Singh B Rousse DR (2017) LyapunovFunction and Sliding Mode Control Approach for the Solar-PV Grid InterfaceSystem IEEE Transactions on Industrial Electronics 64 785-795

17 Kolesnikov AA (2000) Modern applied control theory Synergetic Approach inControl Theory TRTU Moscow Taganrog pp 4477-4479

18 Utkin VI (1977) Variable structure systems with sliding mode IEEE Transactions on Automatic Control 22 212-222

19 Abderrezek H Harmas MN (2016) Comparison study between the terminalsliding mode control and the terminal synergetic control using PSO for DC-DCconverter 4th International Conference on Electrical Engineering (ICEE)

20 Attoui H Khaber F Melhaoui M Kassmi K Essounbouli N (2016) Development and experimentation of a new MPPT synergetic control for photovoltaicsystems Journal of Optoelectronics and Advanced Materials 18 165-173

21 Salmi T Bouzguenda M Gastli A Masmoudi A (2012) MATLABSimulinkBased Modelling of Solar Photovoltaic Cell International Journal of Renewable Energy Research- IJRER

22 Pandiarajan N Muthu R (2011) Mathematical modelling of photovoltaic module with Simulink 1st International Conference on Electrical Energy Systems

23 Kumari JS Babu CS (2012) Mathematical Modeling and Simulation ofPhotovoltaic Cell using Matlab-Simulink Environment International Journal ofElectrical and Computer Engineering (IJECE) 2 26-34

24 Mehimmedetsi B Chenni R (2016) Modelling of DC PV system with MPPT 3rd International Renewable and Sustainable Energy Conference (IRSEC)

25 Ramos-Hernanz JA Campayo JJ Larranaga J Zulueta E Barambones O et al (2012) Two photovoltaic cell simulation models in matlabSimulinkInternational Journal on Technical and Physical Problems of Engineering(IJTPE) 4 45-51

26 Bendiba B Krim F Belmilia H Almia MF Bouloumaa S (2014) Advanced Fuzzy MPPT Controller for a Stand-alone PV System Energy Procedia pp 383-392

27 Jiang Z (2007) Design of power system stabilizers using synergetic control theory IEEE Power Engineering Society General Meeting

28 Laribi M Aiumlt Cheikh MS Larbegraves C Barazane L (2010) Application de lacommande synergetique au controcircle de vitesse drsquoune machine asynchroneRevue des Energies Renouvelables 13 485-496

29 Santi E Monti A Li D Proddutur K Dougal RA (2004) Synergetic Control forPower Electronics Applications A Comparison with the Sliding Mode Approach Journal of Circuits Systems and Computers

30 Santi E Monti A Li D Proddutur K Dougal R (2003) Synergetic control fordc-dc boost converter implementation option IEEE Transactions on industryapplications 39 1803-1813

31 Bezuglov A Kolesnikov A Kondratiev I Vargas J (2005) Synergetic ControlTheory Approach For Solving Systems Of Nonlinear Equations World Multi-Conference Systemics Cybernetics and Informatics

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 6 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

To evaluate the effectiveness of proposed MPPT We consider the PV cell with irradiance is 1000Wm2 and temperature is 25degC The simulation results of the output power the PV panel voltage the output voltage and the PV panel current are shown in Figures10a-10c show the duty cycle and the macro-variable

The photovoltaic system is dependent on the temperature and irradiation conditions and the power will be maximum for along the variations of temperature and irradiation in the PV panel which is giving to input to DC-DC converter Therefore we will evaluate the robustness of the proposed MPPT according to temperature and irradiance variation In each figure two different values of temperature

or irradiance are presented in order to show the robustness (Figures 11-14)

All the obtained results show that the use of synergetic MPPT controller is effective The SC ensures very fast convergence to the MPP and there are no oscillations around the MPP Moreover it provides a high robustness with the variation of the external conditions (temperature and solar irradiance)

ConclusionIn this paper a whole PV system with optimal control strategy

has been presented The Synergetic control is formulated and applied to the PV system This system consists of a solar panel DC-DC boost converter synergetic MPPT controller and an output load The effectiveness and the robustness of the proposed MPPT are proven by simulation results

It is proved using Simulation MatlabSimulink that the designed SC showed good results as it successfully and precisely tracked the MPP with a significantly higher efficiency Hence synergetic control eliminates chattering effects and robust to abrupt change of solar radiation and temperature

L 480 (mH)R 5 (Ω)K 138e-23 (JK)Q 16e-19 (C)Rs 018 (Ω)Rp 360 (Ω)N 36T 0003

Table 2 System specifications

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002600

650

700

750

800

850

900

950

1000

1050

1100

Time (S)

)2m

W( ecnaidarrI

Figure 11 Solar irradiance variation

0 0002 0004 0006 0008 001 0012 0014 0016 0018 0020

10

20

30

40

50

60

70

Time (S)

PpvV0VpvIpv

Ppv

(W)

V0

(V)

Vpv

(V)

Ipv

(A)

Figure 12 Simulation with step irradiance change (1000Wm2 T=25degC)

0 0002 0004 0006 0008 001 0012 0014 0016 0018 002295

300

305

310

315

320

325

Time (S)

)K( erutarepmeT

Figure 13 Temperature variation

0 0002 0004 0006 0008 001 0012 0014 0016 0018 0020

10

20

30

40

50

60

70

Time (S)

)A( vpI )V( vpV )V( 0V )W( vpP

PpvV0VpvIpv

Figure 14 Simulation with step irradiance change (1000Wm2 T=25degC)

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 7 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

In further work these results will be experimentally validated

References

1 Kachhiya K Lokhande M Patel M (2011) Matlabsimulink model of solarPV module and MPPT algorithm National Conference on Recent Trends inEngineering and Technology

2 Rao GJ Mangal DK Shrivastava SK Baig MG (2016) Modeling and Simulation of Incremental Conductance Maximum Power Point Tracking (MPPT) Algorithm for Solar PV Array Using Boost Converter IJSRSET

3 Atik L Petit P Sawicki JP Ternifi ZT Bachir G et al (2016) Comparison of four MPPT techniques for PV systems AIP Conference Proceedings 1758(1)10106314959443

4 Zegaoui A Aillerie M Petit P Sawick JP Charles JP et al (2011) Dynamic behaviour of PV generator trackers under irradiation and temperature changes Solar Energy 85 2953-2964

5 Zegaoui A Aillerie M Petit P Sawick JP Jaafar A et al (2011) Comparison of Two Common Maximum Power Point Trackers by Simulating of PV Generators Energy Procedia 6 678-687

6 Belkaid A Gaubert JP Gherbi A (2016) An Improved Sliding Mode Controlfor Maximum Power Point Tracking in Photovoltaic Systems CEAI 18 86-94

7 Gomes de Brito MA Galotto L Sampaio LP Melo GA Canesin CA et al(2013) Evaluation of the Main MPPT Techniques for Photovoltaic Applications IEEE Transactions on Industrial Electronics 60 1156-1167

8 Jiang Y Abu Qahouq JA Haskew TA (2013) Adaptive Step Size withAdaptive-Perturbation-Frequency Digital MPPT Controller for a Single-SensorPhotovoltaic Solar System IEEE Transactions on Power Electronics 28 3195-3205

9 Kollimalla SK Mishra MK (2013) A new adaptive PampO MPPT algorithm basedon FSCC method for photovoltaic system International Conference on Circuits Power and Computing Technologies (ICCPCT) pp 20-21

10 Murtaza AF Sher HA Chiaberge M Boero D Giuseppe MD et al (2013) Anovel hybrid MPPT technique for solar PV applications using perturb amp observe and Fractional Open Circuit Voltage techniques 15th International Conference Mechatronika

11 Esram T Chapman PL (2007) Comparison of Photovoltaic Array MaximumPower Point Tracking Techniques IEEE Transactions on Energy Conversion22 439-449

12 Reisia AR Moradib MH Jamasb S (2013) Classification and comparison of maximum power point tracking techniques for photovoltaic system Renewable and Sustainable Energy Reviews 19 433-443

13 Subudhi B Pradhan R (2013) A Comparative Study on Maximum Power PointTracking Techniques for Photovoltaic Power Systems IEEE Transactions onSustainable Energy 4 89-98

14 Fan L YU Y (2011) Adaptive Non-singular Terminal Sliding Mode Control forDC-DC Converters Advances in Electrical and Computer Engineering 11119-122

15 Romdhane NMB Damak T (2011) Adaptive Terminal Sliding Mode Control for

Rigid Robotic Manipulators International Journal of Automation and Computing 8 215-220

16 Rezkallah M Sharma SK Chandra A Singh B Rousse DR (2017) LyapunovFunction and Sliding Mode Control Approach for the Solar-PV Grid InterfaceSystem IEEE Transactions on Industrial Electronics 64 785-795

17 Kolesnikov AA (2000) Modern applied control theory Synergetic Approach inControl Theory TRTU Moscow Taganrog pp 4477-4479

18 Utkin VI (1977) Variable structure systems with sliding mode IEEE Transactions on Automatic Control 22 212-222

19 Abderrezek H Harmas MN (2016) Comparison study between the terminalsliding mode control and the terminal synergetic control using PSO for DC-DCconverter 4th International Conference on Electrical Engineering (ICEE)

20 Attoui H Khaber F Melhaoui M Kassmi K Essounbouli N (2016) Development and experimentation of a new MPPT synergetic control for photovoltaicsystems Journal of Optoelectronics and Advanced Materials 18 165-173

21 Salmi T Bouzguenda M Gastli A Masmoudi A (2012) MATLABSimulinkBased Modelling of Solar Photovoltaic Cell International Journal of Renewable Energy Research- IJRER

22 Pandiarajan N Muthu R (2011) Mathematical modelling of photovoltaic module with Simulink 1st International Conference on Electrical Energy Systems

23 Kumari JS Babu CS (2012) Mathematical Modeling and Simulation ofPhotovoltaic Cell using Matlab-Simulink Environment International Journal ofElectrical and Computer Engineering (IJECE) 2 26-34

24 Mehimmedetsi B Chenni R (2016) Modelling of DC PV system with MPPT 3rd International Renewable and Sustainable Energy Conference (IRSEC)

25 Ramos-Hernanz JA Campayo JJ Larranaga J Zulueta E Barambones O et al (2012) Two photovoltaic cell simulation models in matlabSimulinkInternational Journal on Technical and Physical Problems of Engineering(IJTPE) 4 45-51

26 Bendiba B Krim F Belmilia H Almia MF Bouloumaa S (2014) Advanced Fuzzy MPPT Controller for a Stand-alone PV System Energy Procedia pp 383-392

27 Jiang Z (2007) Design of power system stabilizers using synergetic control theory IEEE Power Engineering Society General Meeting

28 Laribi M Aiumlt Cheikh MS Larbegraves C Barazane L (2010) Application de lacommande synergetique au controcircle de vitesse drsquoune machine asynchroneRevue des Energies Renouvelables 13 485-496

29 Santi E Monti A Li D Proddutur K Dougal RA (2004) Synergetic Control forPower Electronics Applications A Comparison with the Sliding Mode Approach Journal of Circuits Systems and Computers

30 Santi E Monti A Li D Proddutur K Dougal R (2003) Synergetic control fordc-dc boost converter implementation option IEEE Transactions on industryapplications 39 1803-1813

31 Bezuglov A Kolesnikov A Kondratiev I Vargas J (2005) Synergetic ControlTheory Approach For Solving Systems Of Nonlinear Equations World Multi-Conference Systemics Cybernetics and Informatics

Citation Mars N Grouz F Essounbouli N Sbita L (2017) Synergetic MPPT Controller for Photovoltaic System J Electr Electron Syst 6 232 doi 1041722332-07961000232

Page 7 of 7

Volume 6 bull Issue 2 bull 1000232J Electr Electron Syst an open access journalISSN 2332-0796

In further work these results will be experimentally validated

References

1 Kachhiya K Lokhande M Patel M (2011) Matlabsimulink model of solarPV module and MPPT algorithm National Conference on Recent Trends inEngineering and Technology

2 Rao GJ Mangal DK Shrivastava SK Baig MG (2016) Modeling and Simulation of Incremental Conductance Maximum Power Point Tracking (MPPT) Algorithm for Solar PV Array Using Boost Converter IJSRSET

3 Atik L Petit P Sawicki JP Ternifi ZT Bachir G et al (2016) Comparison of four MPPT techniques for PV systems AIP Conference Proceedings 1758(1)10106314959443

4 Zegaoui A Aillerie M Petit P Sawick JP Charles JP et al (2011) Dynamic behaviour of PV generator trackers under irradiation and temperature changes Solar Energy 85 2953-2964

5 Zegaoui A Aillerie M Petit P Sawick JP Jaafar A et al (2011) Comparison of Two Common Maximum Power Point Trackers by Simulating of PV Generators Energy Procedia 6 678-687

6 Belkaid A Gaubert JP Gherbi A (2016) An Improved Sliding Mode Controlfor Maximum Power Point Tracking in Photovoltaic Systems CEAI 18 86-94

7 Gomes de Brito MA Galotto L Sampaio LP Melo GA Canesin CA et al(2013) Evaluation of the Main MPPT Techniques for Photovoltaic Applications IEEE Transactions on Industrial Electronics 60 1156-1167

8 Jiang Y Abu Qahouq JA Haskew TA (2013) Adaptive Step Size withAdaptive-Perturbation-Frequency Digital MPPT Controller for a Single-SensorPhotovoltaic Solar System IEEE Transactions on Power Electronics 28 3195-3205

9 Kollimalla SK Mishra MK (2013) A new adaptive PampO MPPT algorithm basedon FSCC method for photovoltaic system International Conference on Circuits Power and Computing Technologies (ICCPCT) pp 20-21

10 Murtaza AF Sher HA Chiaberge M Boero D Giuseppe MD et al (2013) Anovel hybrid MPPT technique for solar PV applications using perturb amp observe and Fractional Open Circuit Voltage techniques 15th International Conference Mechatronika

11 Esram T Chapman PL (2007) Comparison of Photovoltaic Array MaximumPower Point Tracking Techniques IEEE Transactions on Energy Conversion22 439-449

12 Reisia AR Moradib MH Jamasb S (2013) Classification and comparison of maximum power point tracking techniques for photovoltaic system Renewable and Sustainable Energy Reviews 19 433-443

13 Subudhi B Pradhan R (2013) A Comparative Study on Maximum Power PointTracking Techniques for Photovoltaic Power Systems IEEE Transactions onSustainable Energy 4 89-98

14 Fan L YU Y (2011) Adaptive Non-singular Terminal Sliding Mode Control forDC-DC Converters Advances in Electrical and Computer Engineering 11119-122

15 Romdhane NMB Damak T (2011) Adaptive Terminal Sliding Mode Control for

Rigid Robotic Manipulators International Journal of Automation and Computing 8 215-220

16 Rezkallah M Sharma SK Chandra A Singh B Rousse DR (2017) LyapunovFunction and Sliding Mode Control Approach for the Solar-PV Grid InterfaceSystem IEEE Transactions on Industrial Electronics 64 785-795

17 Kolesnikov AA (2000) Modern applied control theory Synergetic Approach inControl Theory TRTU Moscow Taganrog pp 4477-4479

18 Utkin VI (1977) Variable structure systems with sliding mode IEEE Transactions on Automatic Control 22 212-222

19 Abderrezek H Harmas MN (2016) Comparison study between the terminalsliding mode control and the terminal synergetic control using PSO for DC-DCconverter 4th International Conference on Electrical Engineering (ICEE)

20 Attoui H Khaber F Melhaoui M Kassmi K Essounbouli N (2016) Development and experimentation of a new MPPT synergetic control for photovoltaicsystems Journal of Optoelectronics and Advanced Materials 18 165-173

21 Salmi T Bouzguenda M Gastli A Masmoudi A (2012) MATLABSimulinkBased Modelling of Solar Photovoltaic Cell International Journal of Renewable Energy Research- IJRER

22 Pandiarajan N Muthu R (2011) Mathematical modelling of photovoltaic module with Simulink 1st International Conference on Electrical Energy Systems

23 Kumari JS Babu CS (2012) Mathematical Modeling and Simulation ofPhotovoltaic Cell using Matlab-Simulink Environment International Journal ofElectrical and Computer Engineering (IJECE) 2 26-34

24 Mehimmedetsi B Chenni R (2016) Modelling of DC PV system with MPPT 3rd International Renewable and Sustainable Energy Conference (IRSEC)

25 Ramos-Hernanz JA Campayo JJ Larranaga J Zulueta E Barambones O et al (2012) Two photovoltaic cell simulation models in matlabSimulinkInternational Journal on Technical and Physical Problems of Engineering(IJTPE) 4 45-51

26 Bendiba B Krim F Belmilia H Almia MF Bouloumaa S (2014) Advanced Fuzzy MPPT Controller for a Stand-alone PV System Energy Procedia pp 383-392

27 Jiang Z (2007) Design of power system stabilizers using synergetic control theory IEEE Power Engineering Society General Meeting

28 Laribi M Aiumlt Cheikh MS Larbegraves C Barazane L (2010) Application de lacommande synergetique au controcircle de vitesse drsquoune machine asynchroneRevue des Energies Renouvelables 13 485-496

29 Santi E Monti A Li D Proddutur K Dougal RA (2004) Synergetic Control forPower Electronics Applications A Comparison with the Sliding Mode Approach Journal of Circuits Systems and Computers

30 Santi E Monti A Li D Proddutur K Dougal R (2003) Synergetic control fordc-dc boost converter implementation option IEEE Transactions on industryapplications 39 1803-1813

31 Bezuglov A Kolesnikov A Kondratiev I Vargas J (2005) Synergetic ControlTheory Approach For Solving Systems Of Nonlinear Equations World Multi-Conference Systemics Cybernetics and Informatics